Scottish ministers claim that thousands of European students are exploiting Scotland's free university system to avoid paying escalating fees in their home countries.

The latest admissions figures show the number of students from other EU countries taking up places at Scottish universities has nearly doubled in a decade to almost 16,000 last year, at a cost of nearly £75m.

Mike Russell, the Scottish education minister, said the figures showed that European students were becoming an increasingly significant drain on the university sector at a time of deepening cuts in public spending.

Russell is to press Europe's education commissioner, Androulla Vassiliou, to change European university funding rules since the cost had now increased five-fold in the last decade. The number of EU students getting free places went up 17% in 2009/10. By comparison, the number of EU students taking up places at English universities went up by 6%.

Because university education is free for residents of Scotland, under EU law students from all other EU member states are entitled to the same free places. Students in some countries such as France face annual fees and other costs running to thousands of euros a year.

But under a quirk of European law and the UK's system of devolved government, English students are not able to attend for free because they are regarded as citizens of the same member state as Scotland – the UK.

Russell said the current situation was untenable. "Scottish universities have always been cosmopolitan institutions – that is part of their attraction – but we cannot allow them to become a cheap option for students who have to pay to go to university in their home countries," he said.

Russell's demands are designed to help his Scottish National party government fend off increasing pressure from opposition parties and university principals in Scotland to consider new graduate fees to help increase income for universities.

Scottish principals fear their institutions will suffer when English universities begin charging fees of up to £9,000 a year by 2012, increasing their spending power.

The Scottish government has repeatedly rejected calls for new charges or levies on graduates. Alex Salmond, the first minister, plans to make this policy one of the central issues in May's Scottish parliament elections.

Ministers have also been accused of a lack of funding for higher education, forcing courses to close and colleges to sack lecturing staff. Liam Burns, the president of the National Union of Students Scotland, said Russell was trying to avoid that issue.

"It'd be far too easy to write off the huge cultural and economic benefit of welcoming international students in Scotland," Burns said. "If we are to have a debate about the numbers of EU students that come to Scotland we should have it in a rational way, not in a way that diverts attention from the need to increase investment in education in Scotland."

He said today's figures showed that the availability of university places was the real issue. Although enrolments went up by 3%, demand increased by 6%. "This will mean thousands of talented, willing and able people will have seen the opportunity of going to university denied to them," he said.

Recent surveys showed that most EU students in Scotland came from Ireland, where fees are up to €7,474 (£6,290) a year, France, where fees can range from a few hundred to thousands of euros, and Germany, where universities are free in some states but in others cost at least €1,000 a year, plus other charges.